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Let's define variables to represent the amounts invested in each type of account:

- Let $ S $ be the amount invested in stocks.
- Let $ B $ be the amount invested in bonds.
- Let $ C $ be the amount invested in CDs.

We are given the following information:

1. The total amount invested is \$135,000:
   \[
   S + B + C = 135,000
   \]

2. The interest rates for each type of investment:
   - CDs: 4.5% interest.
   - Bonds: 3.2% interest.
   - Stocks: 8.1% interest.

3. The annual income from the investments is \$8,125, so the total interest earned is:
   \[
   0.081S + 0.032B + 0.045C = 8,125
   \]

4. Maricopa Success invests \$40,000 more in bonds than in CDs:
   \[
   B = C + 40,000
   \]

Now, we have a system of three equations:
1. $ S + B + C = 135,000 $
2. $ 0.081S + 0.032B + 0.045C = 8,125 $
3. $ B = C + 40,000 $

We can solve this system of equations to find the values of $ S $, $ B $, and $ C $.

### Step 1: Substitute $ B = C + 40,000 $ into the first two equations.
From the first equation:
\[
S + (C + 40,000) + C = 135,000
\]
Simplifying:
\[
S + 2C + 40,000 = 135,000
\]
\[
S + 2C = 95,000 \quad \text{(Equation 4)}
\]

From the second equation:
\[
0.081S + 0.032(C + 40,000) + 0.045C = 8,125
\]
Simplifying:
\[
0.081S + 0.032C + 1,280 + 0.045C = 8,125
\]
\[
0.081S + 0.077C = 6,845 \quad \text{(Equation 5 after subtracting 1,280 from both sides)}
\]

### Step 2: Solve the system of two equations (Equation 4 and Equation 5).

From Equation 4:
\[
S = 95,000 - 2C
\]
Substitute $ S = 95,000 - 2C $ into Equation 5:
\[
0.081(95,000 - 2C) + 0.077C = 6,845
\]
Simplifying:
\[
7,695 - 0.162C + 0.077C = 6,845
\]
\[
7,695 - 0.085C = 6,845
\]
\[
0.085C = 850
\]
\[
C = \frac{850}{0.085} = 10,000
\]

### Step 3: Find $ B $ and $ S $.
Now that we know $ C = 10,000 $, substitute this into the equation for $ B $:
\[
B = C + 40,000 = 10,000 + 40,000 = 50,000
\]
Substitute $ C = 10,000 $ into the equation for $ S $:
\[
S = 95,000 - 2(10,000) = 95,000 - 20,000 = 75,000
\]

### Final Answer:
- Maricopa Success invested \$75,000 in stocks.
- Maricopa Success invested \$50,000 in bonds.
- Maricopa Success invested \$10,000 in CDs.

Would you like further details on any of the steps? 

Here are some related questions you could explore:
1. How can I verify the solution by plugging values into the original equations?
2. How does the interest rate impact the total income?
3. What if the interest rate for stocks changes—how would that affect the investments?
4. Can this method be applied to other investment portfolios?
5. How would different constraints (e.g., bonds not exceeding a certain amount) affect the solution?

**Tip:** When solving systems of equations, it's helpful to reduce the number of variables step by step using substitution or elimination techniques.

Maricopa's Success scholarship fund receives a gift of $135,000. The money is invested in stocks, bonds, and CDs. CDs pay 4.5% interest, bonds pay 3.2% interest, and stocks pay 8.1% interest. Maricopa Success invests $40,000 more in bonds than in CDs. If the annual income from the investments is $8,125, how much was invested in each account?

Learn how to solve an investment allocation problem where $135,000 is invested in stocks, bonds, and CDs with different interest rates. This detailed step-by-step solution explains how to use systems of equations to determine how much is invested in each account. Suitable for students in Grades 9-12.

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